Determinants of Laplacians on converging hyperbolic surfaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909979832745984 |
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| author | Gross, Renan Lachman, Guy Nachmias, Asaf |
| author_facet | Gross, Renan Lachman, Guy Nachmias, Asaf |
| contents | Let $S_k$ be a sequence of compact hyperbolic surfaces of increasing volume which locally converges to a random rooted surface. We show that if the normalized sum of the reciprocal lengths of very short simple closed geodesics converges to 0, then the normalized logarithm of the determinant of the Laplacian of $S_k$ converges to a constant depending only the law of the limiting surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00338 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Determinants of Laplacians on converging hyperbolic surfaces Gross, Renan Lachman, Guy Nachmias, Asaf Spectral Theory Probability Let $S_k$ be a sequence of compact hyperbolic surfaces of increasing volume which locally converges to a random rooted surface. We show that if the normalized sum of the reciprocal lengths of very short simple closed geodesics converges to 0, then the normalized logarithm of the determinant of the Laplacian of $S_k$ converges to a constant depending only the law of the limiting surface. |
| title | Determinants of Laplacians on converging hyperbolic surfaces |
| topic | Spectral Theory Probability |
| url | https://arxiv.org/abs/2601.00338 |